This chapter examines the control system required to lock the spacecraft onto a specific target while it is moving at varying speeds and in different directions in orbit. The spacecraft position, velocity and acceleration data are constantly needed to orient the spacecraft to nadir point which is considered the centre of the Earth. Euler angles are used to obtain the transformations between the spacecraft’s body reference frame and the Earth-centred inertial frame. Since the spacecraft is constantly in motion, Euler transformations are performed consistently, and a target reference frame are obtained from spacecraft to inertial frame. A dynamic model of a spacecraft with three reaction wheels was developed for system dynamics. The PI control method was applied to enable spacecraft to perform target manoeuvres determined by transformation matrices while moving at varying speeds and accelerations. The differences between the target reference axis and the body reference axis were considered as errors and attempts were made to eliminate these errors using PI control. The results obtained show that the PI controller performs well in tracking the target point in three axes for a spacecraft in an elliptical orbit.